double evalFunctional2D(pInstance instance, double step){
double J;
pTria pt;
int k, icase, ret, ielem, i,ref;
double cb[3], area, *a, *b, *c, ag[3], bg[3], cg[3], q[2], dist;
/* evaluate J*/
J = 0;
for (k = 1; k <= instance->mesh_omega0.nt; k++) {
pt = &instance->mesh_omega0.tria[k];
ref = getRefel(&instance->mesh_omega0,pt->ref);
if(!ref){
a = &instance->mesh_omega0.point[pt->v[0]].c[0];
b = &instance->mesh_omega0.point[pt->v[1]].c[0];
c = &instance->mesh_omega0.point[pt->v[2]].c[0];
for (i = 0; i < 2; i++) {
ag[i] = a[i] + step*instance->sol_omega0.u[2*(pt->v[0]-1)+i];
bg[i] = b[i] + step*instance->sol_omega0.u[2*(pt->v[1]-1)+i];
cg[i] = c[i] + step*instance->sol_omega0.u[2*(pt->v[2]-1)+i];
}
area = area_2d(ag, bg, cg);
if (area <= 0) {
return 1;
}
/* Gauss rule with 1 node */
q[0] = (ag[0]+bg[0]+cg[0])/3;
q[1] = (ag[1]+bg[1]+cg[1])/3;
if (q[0] < 0 || q[0] > 1 || q[1] < 0 || q[1] > 1) {
J += area;
}
else {
icase = buckin(&instance->mesh_distance,&instance->bucket,q);
ielem = locelt(&instance->mesh_distance,icase,q,cb);
if (ielem) {
ret = intpp1(&instance->sol_distance,instance->mesh_distance.tria[ielem].v,&dist,ielem,cb);
if (!ret) exit(1);
instance->sol_omega0.d[pt->v[0]] = dist;
}
J += area*dist;
}
}
}
fprintf(out,"%e \n",J);
return J;
}
/* build right hand side vector and set boundary conds. */
static double *rhsF_P1_2d(LSst *lsst) {
pTria pt;
pEdge pa;
pPoint ppt;
pCl pcl;
double *F,*vp,area,lon,n[2],w[2],*a,*b,*c;
int i,k,nc;
if ( lsst->info.verb == '+' ) fprintf(stdout," gravity and body forces\n");
F = (double*)calloc(lsst->info.dim * lsst->info.np,sizeof(double));
assert(F);
/* gravity as external force */
if ( lsst->sol.cltyp & Gravity ) {
nc = 0;
for (k=1; k<=lsst->info.nt; k++) {
pt = &lsst->mesh.tria[k];
/* measure of K */
a = &lsst->mesh.point[pt->v[0]].c[0];
b = &lsst->mesh.point[pt->v[1]].c[0];
c = &lsst->mesh.point[pt->v[2]].c[0];
area = area_2d(a,b,c) / 3.0;
for (i=0; i<3; i++) {
F[2*(pt->v[i]-1)+0] += area * lsst->sol.gr[0];
F[2*(pt->v[i]-1)+1] += area * lsst->sol.gr[1];
}
nc++;
}
if ( lsst->info.verb == '+' ) fprintf(stdout," %d gravity values assigned\n",nc);
}
/* nodal boundary conditions */
if ( lsst->sol.clelt & LS_ver ) {
nc = 0;
for (k=1; k<=lsst->info.np; k++) {
ppt = &lsst->mesh.point[k];
pcl = getCl(&lsst->sol,ppt->ref,LS_ver);
if ( !pcl ) continue;
else if ( pcl->typ == Dirichlet ) {
vp = pcl->att == 'f' ? &lsst->sol.u[2*(k-1)] : &pcl->u[0];
F[2*(k-1)+0] = LS_TGV * vp[0];
F[2*(k-1)+1] = LS_TGV * vp[1];
}
else if ( pcl->typ == Load ) {
vp = pcl->att == 'f' ? &lsst->sol.u[2*(k-1)] : &pcl->u[0];
F[2*(k-1)+0] = vp[0];
F[2*(k-1)+1] = vp[1];
}
nc++;
}
if ( lsst->info.verb == '+' && nc > 0 ) fprintf(stdout," %d nodal values\n",nc);
}
/* external load along boundary edges */
if ( lsst->sol.clelt & LS_edg ) {
nc = 0;
for (k=1; k<=lsst->info.na; k++) {
pa = &lsst->mesh.edge[k];
pcl = getCl(&lsst->sol,pa->ref,LS_edg);
if ( !pcl ) continue;
else if ( pcl->typ == Dirichlet ) {
for (i=0; i<2; i++) {
vp = pcl->att == 'f' ? &lsst->sol.u[2*(pa->v[i]-1)] : &pcl->u[0];
F[2*(pa->v[i]-1)+0] = LS_TGV * vp[0];
F[2*(pa->v[i]-1)+1] = LS_TGV * vp[1];
}
nc++;
}
/* load along normal direction (normal component) */
else if ( pcl->typ == Load ) {
a = &lsst->mesh.point[pa->v[0]].c[0];
b = &lsst->mesh.point[pa->v[1]].c[0];
lon = length(a,b,n);
if ( pcl->att == 'n' ) {
w[0] = 0.5 * lon * pcl->u[0] * n[0];
w[1] = 0.5 * lon * pcl->u[0] * n[1];
}
else {
vp = pcl->att == 'f' ? &lsst->sol.u[2*(k-1)] : &pcl->u[0];
w[0] = 0.5 * lon * vp[0];
w[1] = 0.5 * lon * vp[1];
}
F[2*(pa->v[0]-1)+0] += w[0];
F[2*(pa->v[0]-1)+1] += w[1];
F[2*(pa->v[1]-1)+0] += w[0];
F[2*(pa->v[1]-1)+1] += w[1];
nc++;
}
}
if ( lsst->info.verb == '+' && nc > 0 ) fprintf(stdout," %d load values\n",nc);
}
return(F);
}